feat(auth): T18 implement user registration endpoint

Add POST /api/auth/register endpoint with:
- UserRegister schema validation
- Email uniqueness check
- Password hashing with bcrypt
- User creation in database
- UserResponse returned (excludes password)

Status: 201 Created on success, 400 for duplicate email, 422 for validation errors

Test coverage: 5 tests for register endpoint

src/openrouter_monitor/main.py

@@ -0,0 +1,43 @@
+"""FastAPI main application.
+
+Main application entry point for OpenRouter API Key Monitor.
+"""
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+
+from openrouter_monitor.config import get_settings
+from openrouter_monitor.routers import auth
+
+settings = get_settings()
+
+# Create FastAPI app
+app = FastAPI(
+    title="OpenRouter API Key Monitor",
+    description="Monitor and manage OpenRouter API keys",
+    version="1.0.0",
+    debug=settings.debug,
+)
+
+# CORS middleware
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=["*"],  # Configure appropriately for production
+    allow_credentials=True,
+    allow_methods=["*"],
+    allow_headers=["*"],
+)
+
+# Include routers
+app.include_router(auth.router, prefix="/api/auth", tags=["authentication"])
+
+
+@app.get("/")
+async def root():
+    """Root endpoint."""
+    return {"message": "OpenRouter API Key Monitor API", "version": "1.0.0"}
+
+
+@app.get("/health")
+async def health_check():
+    """Health check endpoint."""
+    return {"status": "healthy"}